\documentclass[9pt]{article}
\usepackage{amsmath}
\begin{document}
Read in the following dictionary:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{8}   &  11.0 & +  9.00 x_{1} & +  6.00 x_{2} & -10.00 x_{3} & -6.00 x_{4} & +  4.00 x_{5} & -4.00 x_{6} & -9.00 x_{7}\\
 x_{9}   &  50.0 & +  1.00 x_{1} & -7.00 x_{2} & -2.00 x_{3} & -5.00 x_{4} & -4.00 x_{5} & +  3.00 x_{6} & -9.00 x_{7}\\
 x_{10}   &  -7.0 & +  1.00 x_{1} & +  8.00 x_{2} & + 10.00 x_{3} & +  6.00 x_{4} & -8.00 x_{5} & +  9.00 x_{6} & +  2.00 x_{7}\\
 x_{11}   &  -8.0 & +  6.00 x_{1} & -8.00 x_{2} & +  1.00 x_{3} & + 10.00 x_{4} & +  4.00 x_{5} & +  3.00 x_{6} & +  6.00 x_{7}\\
 x_{12}   &  17.0 & -6.00 x_{1} & +  5.00 x_{2} & +  1.00 x_{3} & +  6.00 x_{4} & +  8.00 x_{5} & +  4.00 x_{6} & -10.00 x_{7}\\
 x_{13}   &  -15.0  &   & +  6.00 x_{2} & -9.00 x_{3} & +  8.00 x_{4} & -1.00 x_{5} & +  9.00 x_{6} & +  8.00 x_{7}\\
 x_{14}   &  -2.0 & -1.00 x_{1} & +  2.00 x_{2} & +  3.00 x_{3} & -6.00 x_{4} & +  5.00 x_{5} & +  8.00 x_{6} & +  7.00 x_{7}\\
 x_{15}   &  49.0 & -4.00 x_{1} & -9.00 x_{2} & +  7.00 x_{3} & -3.00 x_{4} & +  3.00 x_{5} &   & -10.00 x_{7}\\
 x_{16}   &  -9.0 & -5.00 x_{1} & + 10.00 x_{2} & +  6.00 x_{3} & +  8.00 x_{4} & +  4.00 x_{5} & + 10.00 x_{6} & -5.00 x_{7}\\
\hline
z    &  0.0 & +  3.00 x_{1} & -3.00 x_{2} & -5.00 x_{3} & -2.00 x_{4} & +  5.00 x_{5} & -5.00 x_{6} & -3.00 x_{7}\\
\end{array}\]
\subsection{Initialization Phase: Dual Problem Solving}
New Objective in primal was changed to : \[ \max\ \sum_{j=1}^{7}\ - x_j \] 
Primal variable $x_j$ corresponds to dual variable $y_j$ for $j = 1,\ldots,16$
Dual Dictionary (with objective changed is): 
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 y_{1}   &  1.0 & -9.00 y_{8} & -1.00 y_{9} & -1.00 y_{10} & -6.00 y_{11} & +  6.00 y_{12} &   & +  1.00 y_{14} & +  4.00 y_{15} & +  5.00 y_{16}\\
 y_{2}   &  1.0 & -6.00 y_{8} & +  7.00 y_{9} & -8.00 y_{10} & +  8.00 y_{11} & -5.00 y_{12} & -6.00 y_{13} & -2.00 y_{14} & +  9.00 y_{15} & -10.00 y_{16}\\
 y_{3}   &  1.0 & + 10.00 y_{8} & +  2.00 y_{9} & -10.00 y_{10} & -1.00 y_{11} & -1.00 y_{12} & +  9.00 y_{13} & -3.00 y_{14} & -7.00 y_{15} & -6.00 y_{16}\\
 y_{4}   &  1.0 & +  6.00 y_{8} & +  5.00 y_{9} & -6.00 y_{10} & -10.00 y_{11} & -6.00 y_{12} & -8.00 y_{13} & +  6.00 y_{14} & +  3.00 y_{15} & -8.00 y_{16}\\
 y_{5}   &  1.0 & -4.00 y_{8} & +  4.00 y_{9} & +  8.00 y_{10} & -4.00 y_{11} & -8.00 y_{12} & +  1.00 y_{13} & -5.00 y_{14} & -3.00 y_{15} & -4.00 y_{16}\\
 y_{6}   &  1.0 & +  4.00 y_{8} & -3.00 y_{9} & -9.00 y_{10} & -3.00 y_{11} & -4.00 y_{12} & -9.00 y_{13} & -8.00 y_{14} &   & -10.00 y_{16}\\
 y_{7}   &  1.0 & +  9.00 y_{8} & +  9.00 y_{9} & -2.00 y_{10} & -6.00 y_{11} & + 10.00 y_{12} & -8.00 y_{13} & -7.00 y_{14} & + 10.00 y_{15} & +  5.00 y_{16}\\
\hline
z    &  -0 & -11.00 y_{8} & -50.00 y_{9} & +  7.00 y_{10} & +  8.00 y_{11} & -17.00 y_{12} & + 15.00 y_{13} & +  2.00 y_{14} & -49.00 y_{15} & +  9.00 y_{16}\\
\end{array}\]
Initialization succeeded in finding final dual dictionary with 5 pivots
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 y_{1}   &  0.909090909091 & -11.00 y_{8} & -7.27 y_{9} & -2.64 y_{10} & +  0.82 y_{4} & +  8.00 y_{12} & -0.73 y_{6} & -9.73 y_{14} & +  1.55 y_{15} & +  4.27 y_{16}\\
 y_{2}   &  0.484848484848 & -5.33 y_{8} & + 19.45 y_{9} & +  0.73 y_{10} & -1.36 y_{4} & -5.67 y_{12} & +  1.88 y_{6} & + 21.21 y_{14} & + 13.09 y_{15} & -2.12 y_{16}\\
 y_{3}   &  1.93939393939 & + 12.67 y_{8} & -5.18 y_{9} & -20.09 y_{10} & +  0.55 y_{4} & -3.67 y_{12} & -1.48 y_{6} & -18.15 y_{14} & -8.64 y_{15} & -16.48 y_{16}\\
 y_{11}   &  0.0151515151515 & +  0.33 y_{8} & +  1.05 y_{9} & +  0.27 y_{10} & -0.14 y_{4} & -0.33 y_{12} & +  0.12 y_{6} & +  1.79 y_{14} & +  0.41 y_{15} & +  0.12 y_{16}\\
 y_{5}   &  1.04545454545 & -5.00 y_{8} & -0.86 y_{9} & +  5.82 y_{10} & +  0.59 y_{4} & -7.00 y_{12} & -0.64 y_{6} & -13.64 y_{14} & -4.77 y_{15} & -5.64 y_{16}\\
 y_{13}   &  0.106060606061 & +  0.33 y_{8} & -0.68 y_{9} & -1.09 y_{10} & +  0.05 y_{4} & -0.33 y_{12} & -0.15 y_{6} & -1.48 y_{14} & -0.14 y_{15} & -1.15 y_{16}\\
 y_{7}   &  0.0606060606061 & +  4.33 y_{8} & +  8.18 y_{9} & +  5.09 y_{10} & +  0.45 y_{4} & + 14.67 y_{12} & +  0.48 y_{6} & -5.85 y_{14} & +  8.64 y_{15} & + 13.48 y_{16}\\
\hline
z    &  1.71212121212 & -3.33 y_{8} & -51.86 y_{9} & -7.18 y_{10} & -0.41 y_{4} & -24.67 y_{12} & -1.30 y_{6} & -5.97 y_{14} & -47.77 y_{15} & -7.30 y_{16}\\
\end{array}\]
Primal Dictionary is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{8}   &  3.33333333333 & + 11.00 x_{1} & +  5.33 x_{2} & -12.67 x_{3} & -0.33 x_{11} & +  5.00 x_{5} & -0.33 x_{13} & -4.33 x_{7}\\
 x_{9}   &  51.8636363636 & +  7.27 x_{1} & -19.45 x_{2} & +  5.18 x_{3} & -1.05 x_{11} & +  0.86 x_{5} & +  0.68 x_{13} & -8.18 x_{7}\\
 x_{10}   &  7.18181818182 & +  2.64 x_{1} & -0.73 x_{2} & + 20.09 x_{3} & -0.27 x_{11} & -5.82 x_{5} & +  1.09 x_{13} & -5.09 x_{7}\\
 x_{4}   &  0.409090909091 & -0.82 x_{1} & +  1.36 x_{2} & -0.55 x_{3} & +  0.14 x_{11} & -0.59 x_{5} & -0.05 x_{13} & -0.45 x_{7}\\
 x_{12}   &  24.6666666667 & -8.00 x_{1} & +  5.67 x_{2} & +  3.67 x_{3} & +  0.33 x_{11} & +  7.00 x_{5} & +  0.33 x_{13} & -14.67 x_{7}\\
 x_{6}   &  1.30303030303 & +  0.73 x_{1} & -1.88 x_{2} & +  1.48 x_{3} & -0.12 x_{11} & +  0.64 x_{5} & +  0.15 x_{13} & -0.48 x_{7}\\
 x_{14}   &  5.9696969697 & +  9.73 x_{1} & -21.21 x_{2} & + 18.15 x_{3} & -1.79 x_{11} & + 13.64 x_{5} & +  1.48 x_{13} & +  5.85 x_{7}\\
 x_{15}   &  47.7727272727 & -1.55 x_{1} & -13.09 x_{2} & +  8.64 x_{3} & -0.41 x_{11} & +  4.77 x_{5} & +  0.14 x_{13} & -8.64 x_{7}\\
 x_{16}   &  7.30303030303 & -4.27 x_{1} & +  2.12 x_{2} & + 16.48 x_{3} & -0.12 x_{11} & +  5.64 x_{5} & +  1.15 x_{13} & -13.48 x_{7}\\
\hline
z    &  -1.71212121212 & -0.91 x_{1} & -0.48 x_{2} & -1.94 x_{3} & -0.02 x_{11} & -1.05 x_{5} & -0.11 x_{13} & -0.06 x_{7}\\
\end{array}\]
Primal Dictionary with original objective is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{8}   &  3.33333333333 & + 11.00 x_{1} & +  5.33 x_{2} & -12.67 x_{3} & -0.33 x_{11} & +  5.00 x_{5} & -0.33 x_{13} & -4.33 x_{7}\\
 x_{9}   &  51.8636363636 & +  7.27 x_{1} & -19.45 x_{2} & +  5.18 x_{3} & -1.05 x_{11} & +  0.86 x_{5} & +  0.68 x_{13} & -8.18 x_{7}\\
 x_{10}   &  7.18181818182 & +  2.64 x_{1} & -0.73 x_{2} & + 20.09 x_{3} & -0.27 x_{11} & -5.82 x_{5} & +  1.09 x_{13} & -5.09 x_{7}\\
 x_{4}   &  0.409090909091 & -0.82 x_{1} & +  1.36 x_{2} & -0.55 x_{3} & +  0.14 x_{11} & -0.59 x_{5} & -0.05 x_{13} & -0.45 x_{7}\\
 x_{12}   &  24.6666666667 & -8.00 x_{1} & +  5.67 x_{2} & +  3.67 x_{3} & +  0.33 x_{11} & +  7.00 x_{5} & +  0.33 x_{13} & -14.67 x_{7}\\
 x_{6}   &  1.30303030303 & +  0.73 x_{1} & -1.88 x_{2} & +  1.48 x_{3} & -0.12 x_{11} & +  0.64 x_{5} & +  0.15 x_{13} & -0.48 x_{7}\\
 x_{14}   &  5.9696969697 & +  9.73 x_{1} & -21.21 x_{2} & + 18.15 x_{3} & -1.79 x_{11} & + 13.64 x_{5} & +  1.48 x_{13} & +  5.85 x_{7}\\
 x_{15}   &  47.7727272727 & -1.55 x_{1} & -13.09 x_{2} & +  8.64 x_{3} & -0.41 x_{11} & +  4.77 x_{5} & +  0.14 x_{13} & -8.64 x_{7}\\
 x_{16}   &  7.30303030303 & -4.27 x_{1} & +  2.12 x_{2} & + 16.48 x_{3} & -0.12 x_{11} & +  5.64 x_{5} & +  1.15 x_{13} & -13.48 x_{7}\\
\hline
z    &  -7.33333333333 & +  1.00 x_{1} & +  3.67 x_{2} & -11.33 x_{3} & +  0.33 x_{11} & +  3.00 x_{5} & -0.67 x_{13} & +  0.33 x_{7}\\
\end{array}\]
\section{Optimization Phase Simplex}
Starting Dictionary is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{8}   &  3.33333333333 & + 11.00 x_{1} & +  5.33 x_{2} & -12.67 x_{3} & -0.33 x_{11} & +  5.00 x_{5} & -0.33 x_{13} & -4.33 x_{7}\\
 x_{9}   &  51.8636363636 & +  7.27 x_{1} & -19.45 x_{2} & +  5.18 x_{3} & -1.05 x_{11} & +  0.86 x_{5} & +  0.68 x_{13} & -8.18 x_{7}\\
 x_{10}   &  7.18181818182 & +  2.64 x_{1} & -0.73 x_{2} & + 20.09 x_{3} & -0.27 x_{11} & -5.82 x_{5} & +  1.09 x_{13} & -5.09 x_{7}\\
 x_{4}   &  0.409090909091 & -0.82 x_{1} & +  1.36 x_{2} & -0.55 x_{3} & +  0.14 x_{11} & -0.59 x_{5} & -0.05 x_{13} & -0.45 x_{7}\\
 x_{12}   &  24.6666666667 & -8.00 x_{1} & +  5.67 x_{2} & +  3.67 x_{3} & +  0.33 x_{11} & +  7.00 x_{5} & +  0.33 x_{13} & -14.67 x_{7}\\
 x_{6}   &  1.30303030303 & +  0.73 x_{1} & -1.88 x_{2} & +  1.48 x_{3} & -0.12 x_{11} & +  0.64 x_{5} & +  0.15 x_{13} & -0.48 x_{7}\\
 x_{14}   &  5.9696969697 & +  9.73 x_{1} & -21.21 x_{2} & + 18.15 x_{3} & -1.79 x_{11} & + 13.64 x_{5} & +  1.48 x_{13} & +  5.85 x_{7}\\
 x_{15}   &  47.7727272727 & -1.55 x_{1} & -13.09 x_{2} & +  8.64 x_{3} & -0.41 x_{11} & +  4.77 x_{5} & +  0.14 x_{13} & -8.64 x_{7}\\
 x_{16}   &  7.30303030303 & -4.27 x_{1} & +  2.12 x_{2} & + 16.48 x_{3} & -0.12 x_{11} & +  5.64 x_{5} & +  1.15 x_{13} & -13.48 x_{7}\\
\hline
z    &  -7.33333333333 & +  1.00 x_{1} & +  3.67 x_{2} & -11.33 x_{3} & +  0.33 x_{11} & +  3.00 x_{5} & -0.67 x_{13} & +  0.33 x_{7}\\
\end{array}\]


 $ x_{1} $ enters and $ x_{4} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{8}   &  8.83333333333 & -13.44 x_{4} & + 23.67 x_{2} & -20.00 x_{3} & +  1.50 x_{11} & -2.94 x_{5} & -0.94 x_{13} & -10.44 x_{7}\\
 x_{9}   &  55.5 & -8.89 x_{4} & -7.33 x_{2} & +  0.33 x_{3} & +  0.17 x_{11} & -4.39 x_{5} & +  0.28 x_{13} & -12.22 x_{7}\\
 x_{10}   &  8.5 & -3.22 x_{4} & +  3.67 x_{2} & + 18.33 x_{3} & +  0.17 x_{11} & -7.72 x_{5} & +  0.94 x_{13} & -6.56 x_{7}\\
 x_{1}   &  0.5 & -1.22 x_{4} & +  1.67 x_{2} & -0.67 x_{3} & +  0.17 x_{11} & -0.72 x_{5} & -0.06 x_{13} & -0.56 x_{7}\\
 x_{12}   &  20.6666666667 & +  9.78 x_{4} & -7.67 x_{2} & +  9.00 x_{3} & -1.00 x_{11} & + 12.78 x_{5} & +  0.78 x_{13} & -10.22 x_{7}\\
 x_{6}   &  1.66666666667 & -0.89 x_{4} & -0.67 x_{2} & +  1.00 x_{3} & -0.00 x_{11} & +  0.11 x_{5} & +  0.11 x_{13} & -0.89 x_{7}\\
 x_{14}   &  10.8333333333 & -11.89 x_{4} & -5.00 x_{2} & + 11.67 x_{3} & -0.17 x_{11} & +  6.61 x_{5} & +  0.94 x_{13} & +  0.44 x_{7}\\
 x_{15}   &  47.0 & +  1.89 x_{4} & -15.67 x_{2} & +  9.67 x_{3} & -0.67 x_{11} & +  5.89 x_{5} & +  0.22 x_{13} & -7.78 x_{7}\\
 x_{16}   &  5.16666666667 & +  5.22 x_{4} & -5.00 x_{2} & + 19.33 x_{3} & -0.83 x_{11} & +  8.72 x_{5} & +  1.39 x_{13} & -11.11 x_{7}\\
\hline
z    &  -6.83333333333 & -1.22 x_{4} & +  5.33 x_{2} & -12.00 x_{3} & +  0.50 x_{11} & +  2.28 x_{5} & -0.72 x_{13} & -0.22 x_{7}\\
\end{array}\]


 $ x_{2} $ enters and $ x_{16} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{8}   &  33.2888888889 & + 11.27 x_{4} & -4.73 x_{16} & + 71.51 x_{3} & -2.44 x_{11} & + 38.34 x_{5} & +  5.63 x_{13} & -63.04 x_{7}\\
 x_{9}   &  47.9222222222 & -16.55 x_{4} & +  1.47 x_{16} & -28.02 x_{3} & +  1.39 x_{11} & -17.18 x_{5} & -1.76 x_{13} & +  4.07 x_{7}\\
 x_{10}   &  12.2888888889 & +  0.61 x_{4} & -0.73 x_{16} & + 32.51 x_{3} & -0.44 x_{11} & -1.33 x_{5} & +  1.96 x_{13} & -14.70 x_{7}\\
 x_{1}   &  2.22222222222 & +  0.52 x_{4} & -0.33 x_{16} & +  5.78 x_{3} & -0.11 x_{11} & +  2.19 x_{5} & +  0.41 x_{13} & -4.26 x_{7}\\
 x_{12}   &  12.7444444444 & +  1.77 x_{4} & +  1.53 x_{16} & -20.64 x_{3} & +  0.28 x_{11} & -0.60 x_{5} & -1.35 x_{13} & +  6.81 x_{7}\\
 x_{6}   &  0.977777777778 & -1.59 x_{4} & +  0.13 x_{16} & -1.58 x_{3} & +  0.11 x_{11} & -1.05 x_{5} & -0.07 x_{13} & +  0.59 x_{7}\\
 x_{14}   &  5.66666666667 & -17.11 x_{4} & +  1.00 x_{16} & -7.67 x_{3} & +  0.67 x_{11} & -2.11 x_{5} & -0.44 x_{13} & + 11.56 x_{7}\\
 x_{15}   &  30.8111111111 & -14.47 x_{4} & +  3.13 x_{16} & -50.91 x_{3} & +  1.94 x_{11} & -21.44 x_{5} & -4.13 x_{13} & + 27.04 x_{7}\\
 x_{2}   &  1.03333333333 & +  1.04 x_{4} & -0.20 x_{16} & +  3.87 x_{3} & -0.17 x_{11} & +  1.74 x_{5} & +  0.28 x_{13} & -2.22 x_{7}\\
\hline
z    &  -1.32222222222 & +  4.35 x_{4} & -1.07 x_{16} & +  8.62 x_{3} & -0.39 x_{11} & + 11.58 x_{5} & +  0.76 x_{13} & -12.07 x_{7}\\
\end{array}\]


 $ x_{3} $ enters and $ x_{15} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{8}   &  76.5670013095 & -9.06 x_{4} & -0.33 x_{16} & -1.40 x_{15} & +  0.29 x_{11} & +  8.22 x_{5} & -0.17 x_{13} & -25.06 x_{7}\\
 x_{9}   &  30.9633347883 & -8.58 x_{4} & -0.26 x_{16} & +  0.55 x_{15} & +  0.32 x_{11} & -5.38 x_{5} & +  0.51 x_{13} & -10.81 x_{7}\\
 x_{10}   &  31.9644260148 & -8.64 x_{4} & +  1.27 x_{16} & -0.64 x_{15} & +  0.80 x_{11} & -15.02 x_{5} & -0.67 x_{13} & +  2.56 x_{7}\\
 x_{1}   &  5.71890004365 & -1.12 x_{4} & +  0.02 x_{16} & -0.11 x_{15} & +  0.11 x_{11} & -0.25 x_{5} & -0.06 x_{13} & -1.19 x_{7}\\
 x_{12}   &  0.250545613269 & +  7.64 x_{4} & +  0.26 x_{16} & +  0.41 x_{15} & -0.51 x_{11} & +  8.10 x_{5} & +  0.32 x_{13} & -4.15 x_{7}\\
 x_{6}   &  0.0229157573112 & -1.14 x_{4} & +  0.04 x_{16} & +  0.03 x_{15} & +  0.05 x_{11} & -0.39 x_{5} & +  0.05 x_{13} & -0.25 x_{7}\\
 x_{14}   &  1.02684417285 & -14.93 x_{4} & +  0.53 x_{16} & +  0.15 x_{15} & +  0.37 x_{11} & +  1.12 x_{5} & +  0.18 x_{13} & +  7.48 x_{7}\\
 x_{3}   &  0.605194238324 & -0.28 x_{4} & +  0.06 x_{16} & -0.02 x_{15} & +  0.04 x_{11} & -0.42 x_{5} & -0.08 x_{13} & +  0.53 x_{7}\\
 x_{2}   &  3.37341772152 & -0.05 x_{4} & +  0.04 x_{16} & -0.08 x_{15} & -0.02 x_{11} & +  0.12 x_{5} & -0.04 x_{13} & -0.17 x_{7}\\
\hline
z    &  3.89589698821 & +  1.90 x_{4} & -0.54 x_{16} & -0.17 x_{15} & -0.06 x_{11} & +  7.95 x_{5} & +  0.06 x_{13} & -7.50 x_{7}\\
\end{array}\]


 $ x_{4} $ enters and $ x_{6} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{8}   &  76.3844086022 & +  7.97 x_{6} & -0.62 x_{16} & -1.65 x_{15} & -0.12 x_{11} & + 11.31 x_{5} & -0.60 x_{13} & -23.11 x_{7}\\
 x_{9}   &  30.7903225806 & +  7.55 x_{6} & -0.53 x_{16} & +  0.32 x_{15} & -0.07 x_{11} & -2.46 x_{5} & +  0.11 x_{13} & -8.96 x_{7}\\
 x_{10}   &  31.7903225806 & +  7.60 x_{6} & +  0.99 x_{16} & -0.87 x_{15} & +  0.41 x_{11} & -12.07 x_{5} & -1.08 x_{13} & +  4.43 x_{7}\\
 x_{1}   &  5.69623655914 & +  0.99 x_{6} & -0.01 x_{16} & -0.14 x_{15} & +  0.06 x_{11} & +  0.14 x_{5} & -0.11 x_{13} & -0.95 x_{7}\\
 x_{12}   &  0.404569892473 & -6.72 x_{6} & +  0.51 x_{16} & +  0.61 x_{15} & -0.17 x_{11} & +  5.49 x_{5} & +  0.69 x_{13} & -5.80 x_{7}\\
 x_{4}   &  0.0201612903226 & -0.88 x_{6} & +  0.03 x_{16} & +  0.03 x_{15} & +  0.04 x_{11} & -0.34 x_{5} & +  0.05 x_{13} & -0.22 x_{7}\\
 x_{14}   &  0.725806451613 & + 13.14 x_{6} & +  0.05 x_{16} & -0.26 x_{15} & -0.29 x_{11} & +  6.21 x_{5} & -0.53 x_{13} & + 10.71 x_{7}\\
 x_{3}   &  0.599462365591 & +  0.25 x_{6} & +  0.05 x_{16} & -0.03 x_{15} & +  0.03 x_{11} & -0.32 x_{5} & -0.09 x_{13} & +  0.59 x_{7}\\
 x_{2}   &  3.37231182796 & +  0.05 x_{6} & +  0.04 x_{16} & -0.08 x_{15} & -0.02 x_{11} & +  0.13 x_{5} & -0.04 x_{13} & -0.16 x_{7}\\
\hline
z    &  3.93413978495 & -1.67 x_{6} & -0.48 x_{16} & -0.12 x_{15} & +  0.03 x_{11} & +  7.30 x_{5} & +  0.15 x_{13} & -7.90 x_{7}\\
\end{array}\]


 $ x_{5} $ enters and $ x_{4} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{8}   &  77.0535211268 & -21.23 x_{6} & +  0.44 x_{16} & -0.75 x_{15} & +  1.37 x_{11} & -33.19 x_{4} & +  0.97 x_{13} & -30.27 x_{7}\\
 x_{9}   &  30.6450704225 & + 13.89 x_{6} & -0.76 x_{16} & +  0.12 x_{15} & -0.39 x_{11} & +  7.20 x_{4} & -0.23 x_{13} & -7.40 x_{7}\\
 x_{10}   &  31.076056338 & + 38.77 x_{6} & -0.14 x_{16} & -1.84 x_{15} & -1.17 x_{11} & + 35.43 x_{4} & -2.76 x_{13} & + 12.07 x_{7}\\
 x_{1}   &  5.70422535211 & +  0.64 x_{6} & -0.00 x_{16} & -0.13 x_{15} & +  0.08 x_{11} & -0.40 x_{4} & -0.10 x_{13} & -1.03 x_{7}\\
 x_{12}   &  0.729577464789 & -20.90 x_{6} & +  1.02 x_{16} & +  1.05 x_{15} & +  0.55 x_{11} & -16.12 x_{4} & +  1.45 x_{13} & -9.28 x_{7}\\
 x_{5}   &  0.0591549295775 & -2.58 x_{6} & +  0.09 x_{16} & +  0.08 x_{15} & +  0.13 x_{11} & -2.93 x_{4} & +  0.14 x_{13} & -0.63 x_{7}\\
 x_{14}   &  1.09295774648 & -2.89 x_{6} & +  0.63 x_{16} & +  0.24 x_{15} & +  0.52 x_{11} & -18.21 x_{4} & +  0.33 x_{13} & +  6.78 x_{7}\\
 x_{3}   &  0.580281690141 & +  1.09 x_{6} & +  0.02 x_{16} & -0.05 x_{15} & -0.02 x_{11} & +  0.95 x_{4} & -0.14 x_{13} & +  0.80 x_{7}\\
 x_{2}   &  3.38028169014 & -0.30 x_{6} & +  0.05 x_{16} & -0.07 x_{15} & -0.00 x_{11} & -0.40 x_{4} & -0.02 x_{13} & -0.24 x_{7}\\
\hline
z    &  4.3661971831 & -20.52 x_{6} & +  0.21 x_{16} & +  0.47 x_{15} & +  0.98 x_{11} & -21.43 x_{4} & +  1.17 x_{13} & -12.53 x_{7}\\
\end{array}\]


 $ x_{11} $ enters and $ x_{10} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{8}   &  113.219449776 & + 23.89 x_{6} & +  0.28 x_{16} & -2.89 x_{15} & -1.16 x_{10} & +  8.04 x_{4} & -2.24 x_{13} & -16.22 x_{7}\\
 x_{9}   &  20.3857965451 & +  1.09 x_{6} & -0.72 x_{16} & +  0.73 x_{15} & +  0.33 x_{10} & -4.49 x_{4} & +  0.68 x_{13} & -11.39 x_{7}\\
 x_{11}   &  26.4683301344 & + 33.02 x_{6} & -0.12 x_{16} & -1.57 x_{15} & -0.85 x_{10} & + 30.17 x_{4} & -2.35 x_{13} & + 10.28 x_{7}\\
 x_{1}   &  7.742162508 & +  3.18 x_{6} & -0.01 x_{16} & -0.25 x_{15} & -0.07 x_{10} & +  1.93 x_{4} & -0.28 x_{13} & -0.24 x_{7}\\
 x_{12}   &  15.3480486244 & -2.67 x_{6} & +  0.96 x_{16} & +  0.19 x_{15} & -0.47 x_{10} & +  0.55 x_{4} & +  0.15 x_{13} & -3.60 x_{7}\\
 x_{5}   &  3.53358925144 & +  1.75 x_{6} & +  0.08 x_{16} & -0.13 x_{15} & -0.11 x_{10} & +  1.03 x_{4} & -0.17 x_{13} & +  0.72 x_{7}\\
 x_{14}   &  14.8714011516 & + 14.30 x_{6} & +  0.57 x_{16} & -0.58 x_{15} & -0.44 x_{10} & -2.50 x_{4} & -0.89 x_{13} & + 12.13 x_{7}\\
 x_{3}   &  0.127959053103 & +  0.52 x_{6} & +  0.02 x_{16} & -0.03 x_{15} & +  0.01 x_{10} & +  0.44 x_{4} & -0.10 x_{13} & +  0.62 x_{7}\\
 x_{2}   &  3.28087012156 & -0.42 x_{6} & +  0.05 x_{16} & -0.06 x_{15} & +  0.00 x_{10} & -0.51 x_{4} & -0.01 x_{13} & -0.28 x_{7}\\
\hline
z    &  30.412028151 & + 11.97 x_{6} & +  0.09 x_{16} & -1.08 x_{15} & -0.84 x_{10} & +  8.26 x_{4} & -1.15 x_{13} & -2.41 x_{7}\\
\end{array}\]


 $ x_{4} $ enters and $ x_{9} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{8}   &  149.722222222 & + 25.84 x_{6} & -1.00 x_{16} & -1.59 x_{15} & -0.57 x_{10} & -1.79 x_{9} & -1.03 x_{13} & -36.61 x_{7}\\
 x_{4}   &  4.53888888889 & +  0.24 x_{6} & -0.16 x_{16} & +  0.16 x_{15} & +  0.07 x_{10} & -0.22 x_{9} & +  0.15 x_{13} & -2.54 x_{7}\\
 x_{11}   &  163.427777778 & + 40.34 x_{6} & -4.93 x_{16} & +  3.32 x_{15} & +  1.37 x_{10} & -6.72 x_{9} & +  2.20 x_{13} & -66.21 x_{7}\\
 x_{1}   &  16.4888888889 & +  3.65 x_{6} & -0.32 x_{16} & +  0.06 x_{15} & +  0.08 x_{10} & -0.43 x_{9} & +  0.01 x_{13} & -5.13 x_{7}\\
 x_{12}   &  17.8222222222 & -2.54 x_{6} & +  0.87 x_{16} & +  0.28 x_{15} & -0.43 x_{10} & -0.12 x_{9} & +  0.23 x_{13} & -4.98 x_{7}\\
 x_{5}   &  8.19444444444 & +  2.00 x_{6} & -0.09 x_{16} & +  0.04 x_{15} & -0.04 x_{10} & -0.23 x_{9} & -0.01 x_{13} & -1.89 x_{7}\\
 x_{14}   &  3.51111111111 & + 13.70 x_{6} & +  0.97 x_{16} & -0.98 x_{15} & -0.63 x_{10} & +  0.56 x_{9} & -1.27 x_{13} & + 18.47 x_{7}\\
 x_{3}   &  2.10555555556 & +  0.63 x_{6} & -0.05 x_{16} & +  0.04 x_{15} & +  0.05 x_{10} & -0.10 x_{9} & -0.03 x_{13} & -0.48 x_{7}\\
 x_{2}   &  0.972222222222 & -0.55 x_{6} & +  0.13 x_{16} & -0.14 x_{15} & -0.03 x_{10} & +  0.11 x_{9} & -0.09 x_{13} & +  1.01 x_{7}\\
\hline
z    &  67.9166666667 & + 13.97 x_{6} & -1.22 x_{16} & +  0.26 x_{15} & -0.23 x_{10} & -1.84 x_{9} & +  0.10 x_{13} & -23.36 x_{7}\\
\end{array}\]


 $ x_{6} $ enters and $ x_{2} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{8}   &  195.64453125 & -47.23 x_{2} & +  5.15 x_{16} & -8.35 x_{15} & -2.19 x_{10} & +  3.56 x_{9} & -5.17 x_{13} & + 11.03 x_{7}\\
 x_{4}   &  4.9703125 & -0.44 x_{2} & -0.10 x_{16} & +  0.10 x_{15} & +  0.06 x_{10} & -0.17 x_{9} & +  0.11 x_{13} & -2.09 x_{7}\\
 x_{11}   &  235.131445312 & -73.75 x_{2} & +  4.69 x_{16} & -7.24 x_{15} & -1.16 x_{10} & +  1.63 x_{9} & -4.26 x_{13} & +  8.17 x_{7}\\
 x_{1}   &  22.976953125 & -6.67 x_{2} & +  0.55 x_{16} & -0.90 x_{15} & -0.15 x_{10} & +  0.33 x_{9} & -0.57 x_{13} & +  1.60 x_{7}\\
 x_{12}   &  13.3158203125 & +  4.64 x_{2} & +  0.26 x_{16} & +  0.94 x_{15} & -0.27 x_{10} & -0.65 x_{9} & +  0.64 x_{13} & -9.65 x_{7}\\
 x_{5}   &  11.7529296875 & -3.66 x_{2} & +  0.39 x_{16} & -0.48 x_{15} & -0.16 x_{10} & +  0.19 x_{9} & -0.34 x_{13} & +  1.80 x_{7}\\
 x_{14}   &  27.853125 & -25.04 x_{2} & +  4.23 x_{16} & -4.57 x_{15} & -1.48 x_{10} & +  3.39 x_{9} & -3.46 x_{13} & + 43.73 x_{7}\\
 x_{3}   &  3.2228515625 & -1.15 x_{2} & +  0.10 x_{16} & -0.12 x_{15} & +  0.01 x_{10} & +  0.03 x_{9} & -0.13 x_{13} & +  0.68 x_{7}\\
 x_{6}   &  1.77734375 & -1.83 x_{2} & +  0.24 x_{16} & -0.26 x_{15} & -0.06 x_{10} & +  0.21 x_{9} & -0.16 x_{13} & +  1.84 x_{7}\\
\hline
z    &  92.75390625 & -25.55 x_{2} & +  2.11 x_{16} & -3.39 x_{15} & -1.10 x_{10} & +  1.05 x_{9} & -2.14 x_{13} & +  2.41 x_{7}\\
\end{array}\]


 $ x_{7} $ enters and $ x_{12} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{8}   &  210.858917301 & -41.94 x_{2} & +  5.45 x_{16} & -7.27 x_{15} & -2.50 x_{10} & +  2.82 x_{9} & -4.44 x_{13} & -1.14 x_{12}\\
 x_{4}   &  2.09121621622 & -1.45 x_{2} & -0.16 x_{16} & -0.10 x_{15} & +  0.12 x_{10} & -0.03 x_{9} & -0.03 x_{13} & +  0.22 x_{12}\\
 x_{11}   &  246.400004046 & -69.83 x_{2} & +  4.91 x_{16} & -6.44 x_{15} & -1.39 x_{10} & +  1.09 x_{9} & -3.72 x_{13} & -0.85 x_{12}\\
 x_{1}   &  25.1879956304 & -5.90 x_{2} & +  0.60 x_{16} & -0.74 x_{15} & -0.20 x_{10} & +  0.22 x_{9} & -0.47 x_{13} & -0.17 x_{12}\\
 x_{7}   &  1.37920780061 & +  0.48 x_{2} & +  0.03 x_{16} & +  0.10 x_{15} & -0.03 x_{10} & -0.07 x_{9} & +  0.07 x_{13} & -0.10 x_{12}\\
 x_{5}   &  14.2419687652 & -2.79 x_{2} & +  0.44 x_{16} & -0.31 x_{15} & -0.21 x_{10} & +  0.07 x_{9} & -0.22 x_{13} & -0.19 x_{12}\\
 x_{14}   &  88.1589860819 & -4.05 x_{2} & +  5.43 x_{16} & -0.31 x_{15} & -2.71 x_{10} & +  0.47 x_{9} & -0.58 x_{13} & -4.53 x_{12}\\
 x_{3}   &  4.1559718401 & -0.82 x_{2} & +  0.12 x_{16} & -0.05 x_{15} & -0.01 x_{10} & -0.01 x_{9} & -0.09 x_{13} & -0.07 x_{12}\\
 x_{6}   &  4.32025813238 & -0.94 x_{2} & +  0.29 x_{16} & -0.08 x_{15} & -0.11 x_{10} & +  0.08 x_{9} & -0.04 x_{13} & -0.19 x_{12}\\
\hline
z    &  96.0726250202 & -24.39 x_{2} & +  2.17 x_{16} & -3.16 x_{15} & -1.17 x_{10} & +  0.89 x_{9} & -1.98 x_{13} & -0.25 x_{12}\\
\end{array}\]


 $ x_{9} $ enters and $ x_{7} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{8}   &  268.964037474 & -21.71 x_{2} & +  6.61 x_{16} & -3.17 x_{15} & -3.68 x_{10} & -42.13 x_{7} & -1.66 x_{13} & -5.51 x_{12}\\
 x_{4}   &  1.41835398408 & -1.68 x_{2} & -0.17 x_{16} & -0.15 x_{15} & +  0.13 x_{10} & +  0.49 x_{7} & -0.06 x_{13} & +  0.27 x_{12}\\
 x_{11}   &  268.795910144 & -62.03 x_{2} & +  5.36 x_{16} & -4.86 x_{15} & -1.84 x_{10} & -16.24 x_{7} & -2.65 x_{13} & -2.53 x_{12}\\
 x_{1}   &  29.7079681676 & -4.33 x_{2} & +  0.69 x_{16} & -0.42 x_{15} & -0.29 x_{10} & -3.28 x_{7} & -0.25 x_{13} & -0.51 x_{12}\\
 x_{9}   &  20.6035055908 & +  7.17 x_{2} & +  0.41 x_{16} & +  1.45 x_{15} & -0.42 x_{10} & -14.94 x_{7} & +  0.99 x_{13} & -1.55 x_{12}\\
 x_{5}   &  15.5825526342 & -2.33 x_{2} & +  0.47 x_{16} & -0.21 x_{15} & -0.24 x_{10} & -0.97 x_{7} & -0.15 x_{13} & -0.29 x_{12}\\
 x_{14}   &  97.7548101138 & -0.71 x_{2} & +  5.62 x_{16} & +  0.37 x_{15} & -2.91 x_{10} & -6.96 x_{7} & -0.12 x_{13} & -5.25 x_{12}\\
 x_{3}   &  3.90561096001 & -0.91 x_{2} & +  0.12 x_{16} & -0.07 x_{15} & -0.01 x_{10} & +  0.18 x_{7} & -0.10 x_{13} & -0.05 x_{12}\\
 x_{6}   &  6.04291326685 & -0.34 x_{2} & +  0.32 x_{16} & +  0.04 x_{15} & -0.15 x_{10} & -1.25 x_{7} & +  0.04 x_{13} & -0.32 x_{12}\\
\hline
z    &  114.457338572 & -17.99 x_{2} & +  2.54 x_{16} & -1.86 x_{15} & -1.55 x_{10} & -13.33 x_{7} & -1.10 x_{13} & -1.63 x_{12}\\
\end{array}\]


 $ x_{16} $ enters and $ x_{4} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{8}   &  323.418373318 & -86.22 x_{2} & -38.39 x_{4} & -9.02 x_{15} & +  1.34 x_{10} & -23.40 x_{7} & -3.89 x_{13} & +  4.73 x_{12}\\
 x_{16}   &  8.23873610298 & -9.76 x_{2} & -5.81 x_{4} & -0.88 x_{15} & +  0.76 x_{10} & +  2.83 x_{7} & -0.34 x_{13} & +  1.55 x_{12}\\
 x_{11}   &  312.919251024 & -114.30 x_{2} & -31.11 x_{4} & -9.60 x_{15} & +  2.23 x_{10} & -1.06 x_{7} & -4.46 x_{13} & +  5.77 x_{12}\\
 x_{1}   &  35.3639555295 & -11.03 x_{2} & -3.99 x_{4} & -1.03 x_{15} & +  0.23 x_{10} & -1.33 x_{7} & -0.48 x_{13} & +  0.56 x_{12}\\
 x_{9}   &  23.9771796372 & +  3.18 x_{2} & -2.38 x_{4} & +  1.09 x_{15} & -0.11 x_{10} & -13.78 x_{7} & +  0.85 x_{13} & -0.91 x_{12}\\
 x_{5}   &  19.4359274429 & -6.89 x_{2} & -2.72 x_{4} & -0.63 x_{15} & +  0.12 x_{10} & +  0.35 x_{7} & -0.31 x_{13} & +  0.44 x_{12}\\
 x_{14}   &  144.086600351 & -55.59 x_{2} & -32.67 x_{4} & -4.61 x_{15} & +  1.36 x_{10} & +  8.98 x_{7} & -2.01 x_{13} & +  3.46 x_{12}\\
 x_{3}   &  4.87829139848 & -2.06 x_{2} & -0.69 x_{4} & -0.18 x_{15} & +  0.08 x_{10} & +  0.52 x_{7} & -0.14 x_{13} & +  0.13 x_{12}\\
 x_{6}   &  8.70450555881 & -3.50 x_{2} & -1.88 x_{4} & -0.25 x_{15} & +  0.10 x_{10} & -0.33 x_{7} & -0.06 x_{13} & +  0.18 x_{12}\\
\hline
z    &  135.357519017 & -42.75 x_{2} & -14.74 x_{4} & -4.11 x_{15} & +  0.38 x_{10} & -6.14 x_{7} & -1.96 x_{13} & +  2.30 x_{12}\\
\end{array}\]


 $ x_{10} $ enters and $ x_{9} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{8}   &  616.914438503 & -47.35 x_{2} & -67.51 x_{4} & +  4.35 x_{15} & -12.24 x_{9} & -192.05 x_{7} & +  6.50 x_{13} & -6.44 x_{12}\\
 x_{16}   &  174.796791444 & + 12.30 x_{2} & -22.33 x_{4} & +  6.70 x_{15} & -6.95 x_{9} & -92.88 x_{7} & +  5.56 x_{13} & -4.79 x_{12}\\
 x_{11}   &  801.181818182 & -49.64 x_{2} & -79.55 x_{4} & + 12.64 x_{15} & -20.36 x_{9} & -281.64 x_{7} & + 12.82 x_{13} & -12.82 x_{12}\\
 x_{1}   &  86.2673796791 & -4.29 x_{2} & -9.04 x_{4} & +  1.29 x_{15} & -2.12 x_{9} & -30.58 x_{7} & +  1.32 x_{13} & -1.38 x_{12}\\
 x_{10}   &  219.128342246 & + 29.02 x_{2} & -21.74 x_{4} & +  9.98 x_{15} & -9.14 x_{9} & -125.92 x_{7} & +  7.75 x_{13} & -8.34 x_{12}\\
 x_{5}   &  44.8235294118 & -3.53 x_{2} & -5.24 x_{4} & +  0.53 x_{15} & -1.06 x_{9} & -14.24 x_{7} & +  0.59 x_{13} & -0.53 x_{12}\\
 x_{14}   &  442.967914439 & -16.01 x_{2} & -62.32 x_{4} & +  9.01 x_{15} & -12.47 x_{9} & -162.77 x_{7} & +  8.56 x_{13} & -7.91 x_{12}\\
 x_{3}   &  23.0855614973 & +  0.35 x_{2} & -2.49 x_{4} & +  0.65 x_{15} & -0.76 x_{9} & -9.95 x_{7} & +  0.50 x_{13} & -0.56 x_{12}\\
 x_{6}   &  29.7326203209 & -0.71 x_{2} & -3.96 x_{4} & +  0.71 x_{15} & -0.88 x_{9} & -12.42 x_{7} & +  0.68 x_{13} & -0.62 x_{12}\\
\hline
z    &  218.828877005 & -31.70 x_{2} & -23.02 x_{4} & -0.30 x_{15} & -3.48 x_{9} & -54.11 x_{7} & +  0.99 x_{13} & -0.88 x_{12}\\
\end{array}\]


 $ x_{13} $ enters and Unbounded Dictionary!


 $ x_{13} $ enters and Unbounded Dictionary!
\end{document}
